PHYSICAL REVIEW B
VOLUME 59, NUMBER 23
15 JUNE 1999-I
Proton-induced kinetic plasmon excitation in Al and Mg
S. M. Ritzau and R. A. Baragiola
University of Virginia, Laboratory for Atomic and Surface Physics, Thornton Hall, Charlottesville, Virginia 22901
R. C. Monreal
Universidad Autónoma de Madrid, Depto. Fı́sica Teórica de la Materia Condensada, C-V, Cantoblanco, 28049 Madrid, Spain
~Received 22 December 1998!
We report energy distributions of electrons emitted from Al and Mg surfaces bombarded by 3–100-keV/amu
hydrogen and deuterium ions. The energy spectra contain structure consistent with the decay of bulk plasmons,
even below the velocity threshold expected from current theories. To explain the results we compare the
importance of additional mechanisms involving electron capture, lattice-assisted excitation, and excitation by
fast secondary electrons. @S0163-1829~99!02423-6#
I. INTRODUCTION
One of the main ways in which fast charged particles lose
energy in condensed matter is by exciting plasmons; collective excitation of valence electrons.1 This mode of energy
loss is especially important for materials of low atomic number Z, and for high-Z materials when the projectile velocity is
insufficient to produce significant inner-shell excitations. In
addition, the most common plasmon decay mechanism, a
single-electron transition, can contribute to the emission of
electrons from the solid.2,3 Although plasmon excitation of
metals by fast ions has attracted several theoretical
studies,3–6 experimental work for fast ion impact at energies
of tens and hundreds of keV ~Refs. 7–11! has been limited to
identifying the plasmon decay structures seen in the electron
emission spectra. In spite of the importance of plasmon excitation in energy loss and as source of electron emission for
fast ions, quantitative studies of the plasmon excitation probabilities have only been done theoretically.
An electron-gas description of valence electrons leads to a
minimum or threshold velocity n th for plasmon excitations
by a moving charge, determined by conservation of energy
and momentum. This is shown with the aid of a diagram of
allowed energy transfer \v vs momentum transfer \k in the
excitation of a gas of free electrons ~Fig. 1!.3 Allowed excitations by heavy particles occur at and below the straight
lines \ v 5k n , which, for projectile velocities n , n th cannot
intersect the plasmon line. For ions with mass much higher
than the electron mass, the threshold velocity for exciting a
narrow plasmon resonance is n th;1.3n F , 3 where n F is the
Fermi velocity. A slightly lower threshold results from the
small plasmon width in metals like Al and Mg. We note that
excitation of plasmons by ions near n th is not constrained by
the available projectile energy, and this makes ions better
suited than electrons for exploring the possible existence of
excitations below the predicted threshold.
To study ion-induced plasmon excitations, we cannot use
the projectile energy-loss method common in studies with
fast electrons.1,12 Characteristic energy losses are not observed with heavy projectiles because they are obscured by
multiple energy losses from collisions with target nuclei. An
0163-1829/99/59~23!/15506~7!/$15.00
PRB 59
alternative method to observe plasmons is through the electrons or photons that result from their decay.12 Since the
radiative channel is very unlikely, we have used electron
spectroscopy for studying plasmon excitation. The characteristic spectral signature allows the separation of electrons
from plasmon decay from those originating from other processes: Auger neutralization of the incoming ion at the
surface,13,14 direct ionizations in ion-atom and ion-electron
collisions, and Auger decay of inner-shell excitations.15 In
the study we report here, we measured electron emission
spectra from clean Al and Mg surfaces bombarded by H1
and D1 ions with incident velocities above and below n th
~3–100 keV/amu!. We observed structure in the energy spectra of electrons even at velocities lower than n th . Below, we
describe the experiments and discuss the discrepancy of the
results with the theoretical expectation. Using simple models, we estimate theoretically the contributions of possible
mechanisms giving rise to plasmon excitation, and compare
these results with experiments.
FIG. 1. The excitation spectrum of a free-electron gas with the
density corresponding to Al, where \v and k are the energy and
momentum transfer, respectively. The shaded area is the domain of
single-particle excitations, and the line corresponds to the plasmon
dispersion in the random-phase approximation. Maximum-energytransfer lines for different proton energies are shown as straight
lines. The points are from electron-energy-loss measurements of the
plasmon resonance ~Ref. 24!.
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©1999 The American Physical Society
PRB 59
PROTON-INDUCED KINETIC PLASMON EXCITATION . . .
15 507
II. EXPERIMENTS
The experiments were carried out in an ultrahigh-vacuum
chamber ~base pressure 8310210 Torr! using a sphericalsector electrostatic analyzer. The pass energy E pass of the
analyzer was set constant at 25 eV ~resolution DE50.2 eV!,
and electrons were accelerated to E pass by a programmable
voltage applied to an entrance electrode. In this mode of
operation, the transmission of the analyzer is approximately
constant over the measured electron energy range. The analyzer work function f a was measured using 100-eV electrons following the procedure outlined in Ref. 16. For purposes of discussion, electron energies are shifted to refer to
the vacuum level of the sample.
A focused, mass-analyzed ion beam from an ion accelerator entered the chamber from a differentially pumped chamber through a 1-mm-diameter aperture. The axis of the analyzer acceptance cone and the normal to the target surface
were collinear, and the incidence angle of the ions was 60°
with respect to this axis. Clean polycrystalline targets where
obtained by vacuum depositing 40–100-nm-thick films from
carefully outgassed Al and Mg ~99.999% pure.! In situ Auger electron spectroscopy with 2.5–3-keV electrons showed
the absence of contaminants above the detection limit of
;1%. To extend the projectile velocity range to lower values, we used deuterium ions, which are expected to be
equivalent to protons of the same velocity, since isotope effects are negligible in electron emission at these velocities.17
Incident electrons were also used to produce the plasmon
decay structures, which were very similar to well-known
electron-excited spectra reported previously.18–20
To accurately measure low-energy electrons, we used
Helmholtz coils and a thin m-metal liner to reduce the magnetic field in the region between the target and the analyzer
to ,2 mG, and biased the target to 25 V. The focusing
effect on the detection efficiency, created by this bias and by
the analyzer electro-optical elements, was checked by calculating electron trajectories.21 The results were used to correct
the collected spectra. We tested this correction by comparing
spectra taken at different sample potentials.
FIG. 2. Electron energy spectra N(E) from Al bombarded by
H1 at 60° incidence. Bottom: derivative spectra dN(E)/dE. Parameter is the ion energy in keV.
introduces a broadening of ;0.5 eV. dN/dE has minima at
E m , from which we can determine the plasmon energy E b .
The measured values of E m are higher than \ v p (k50)
expected for zero-momentum bulk plasmons ~15.3 and 10.6
eV for Al and Mg respectively!, and depend on projectile
energy, as shown in Fig. 4. The shift in the plasmon energy
with impact velocity is related to the plasmon dispersion, as
shown in Fig. 1. In the region where pair excitations are
allowed, the width of the plasmon resonance measured using
electron energy loss is 3–5 times greater than those we see in
the ion-induced secondary electron spectra.24 Another significant finding is that, near n th , the plasmon energy is observed to deviate significantly from the behavior expected
from Fig. 1.
We do not see the surface plasmon clearly resolved from
the peak in the energy distribution due to the surface barrier,
III. RESULTS
Figures 2 and 3 show representative electron energy spectra N(E) obtained from Mg and Al surfaces, respectively.
The spectra are similar to spectra reported in the literature
and obtained under different excitation conditions.7,9,18–20
The spectra were normalized so their integral equals the total
electron yields g, which were measured by us and
elsewhere.22 A prominent shoulder is observed in the N(E)
spectra, similar to that seen for electron impact, which is due
to the decay of bulk plasmons by excitation of a valence
electron ~interband transition! with simultaneous momentum
exchange with the lattice. This process produces an electron
energy distribution with a maximum energy of E m 5E b
2 f , where E b is the energy of the bulk plasmon, and f is
the work function of the target. The maximum energy E m
corresponds to the case where the plasmon is absorbed by an
electron at the Fermi level. The high-energy edge of the
shoulder is broadened by ;2 eV due to the finite plasmon
lifetime.23,24 Figures 2 and 3 also show derivative spectra
dN/dE obtained using the Sawitsky-Golay algorithm, which
FIG. 3. Same as Fig. 2, but for Mg.
15 508
S. M. RITZAU, R. A. BARAGIOLA, AND R. C. MONREAL
PRB 59
integrate N p (E)5N(E)2N t (E) over a small energy region
2 d 52 eV corresponding to the plasmon full width at half
maximum, and calculate the fraction of emitted electrons
which are due to plasmon decay,
f p5
FIG. 4. Plasmon energies derived from the plasmon high-energy
edge, measured in the derivative spectra, vs projectile velocity. Also
shown are data from Ref. 9 ~*! and the RPA predictions ~solid
lines!.
as seen in the spectrum of Hasselkamp and Scharmann for
500-keV H1 impact on Al at normal incidence.9 We attribute
this to the fact that excitation should be low due to our use of
lower velocities and oblique ~60°! incidence.25 The spectra
of Benazeth et al.,15 measured for 60-keV H1 at 60° incidence, also lack this feature. For Mg targets, structure due to
surface plasmon decay occurs at ;3.5 eV and so it cannot be
separated with certainty from the low-energy peak in N(E)
created by the surface barrier.
To quantify the number of electrons emitted due to bulkplasmon decay, we must distinguish them from those due to
all other processes. The method we used is illustrated graphically in Fig. 5. The high-energy continuum tail above E m
1DEm is well represented by a function of the form N t (E)
5BE n , where B and n are constant fitting parameters. We
slightly extrapolate N t (E) to E m to obtain the number of
electrons from plasmon decay, at E m , as N p (E m )5N(E m )
2N t (E m ). Subtraction of a power-law background was used
and justified by Sickafus26 to separate sources of secondary
electrons from the continuum background. To reduce the error associated with the choice of the exact value of E m , we
g p C~ v0!
5
g
g
E
EM1d
Em2d
N p ~ E ! dE,
~1!
where g p is the electron yield due to plasmon decay, and the
factor C( v 0 ) relates the integral of N p (E) about E m over the
range 2d to the integral of N p (E) over all E. Although we do
not know the exact form of N p (E) outside of the region near
E m , we can estimate N p (E) to obtain an approximate result.
We approximate N p (E) using a parabolic density of states
uniformly shifted by E m , and then convoluted with a 2-eVwide Gaussian to account for the plasmon width. We estimate C58 ~Al! and 5 ~Mg!. Because the broadening in the
distribution of secondary electrons is symmetric about E m ,
and the integration width we use always exceeds the plasmon
width, C is independent of primary velocity. Our estimated
values of C for H1 on Al are consistent with the values
obtained from plasmon decay spectra calculated by Rösler,27
divided by cos60° to account for oblique incidence. He
found that, for Al ~Mg!, C( n 0 ) ranges from 5 to 12 ~5 to 3!
for energies from 100 to 1000 keV. Other methods of background subtraction applied to the data, including modeling
the secondary distributions using the theory of Schou28 and
use of the derivative spectra, were found to produce results
with greater uncertainties.
Since f p is determined using N p (E), and the exact shape
of N p (E) is not known, the uncertainty in f p was obtained by
varying the plasmon energy, integral width d, background
level, and value of C( n 0 ), and determining their effect of the
value of f p for representative spectra. For a shift in the plasmon energy E m of 6DE50.7 eV ~the sum of the analyzer
resolution and the broadening due to the numerical derivative algorithm!, we found ( d f p / f p ) E ;0.05. A variation of
the integral width of 0.3, d ,1.5 eV produced ( d f p / f p ) d
;0.07. We assign generous errors of 20% in the background
level evaluated at E m , and an additional 20% uncertainty in
C( n 0 ). Adding all errors in quadrature gives uncertainties
(D f p / f p );0.3 and (D g p / g p );0.32.
Figures 6 and 7 show g p as a function of projectile energy
for Al and Mg, respectively. In them, one can see substantial
plasmon excitation below the predicted threshold n th for both
Al and Mg. The results for Al are compared to the theory by
Rösler3 above n th . The ratio g p / g is consistent with the
value for 500-keV H1 we extract from the data of Ref. 9
using the same procedure described above.
IV. DISCUSSION
FIG. 5. The extraction of the fractional plasmon decay yield,
f p , from a measured spectrum, showing the extrapolated highenergy tail N t (E) which we subtract from the measured N(E) to
obtain N p (E). E m is the position of the local minimum of
dN(E)/dE.
If the observed plasmon excitation below n th results directly from interactions with the projectile, our findings
would imply the need to revise existing theories of plasmon
excitation and electronic energy loss at low velocities. On
the other hand, plasmons may be produced by secondary
processes involving fast electrons resulting from singleparticle excitations. We explore several mechanisms that
may explain the observations. The first is the relaxation of
the energy-momentum conservation criteria for an electron
PRB 59
PROTON-INDUCED KINETIC PLASMON EXCITATION . . .
FIG. 6. Electron yield due to plasmon decay, g p ~electrons/ion!,
as a function of incident energy for proton impact on Al. Also
shown are the theoretical predictions of Rösler ~Ref. 3!, adjusted for
oblique incidence ~dashed line!, the plasmon-assisted electron capture yield g Ap given by Eq. ~5!, and the electron yield due to plasmons excited by energetic secondary electrons g ep from Eq. ~12!.
Also shown are data from Ref. 9 ~*!.
gas, possible if the lattice absorbs momentum during the excitation event by an umklapp process. This mechanism is
unlikely, as judged from the very weak plasmon excitation
by photons in interactions with valence electrons,29 which
require a similar absorption of momentum by the lattice. The
fact that plasmon energies do not deviate much from the k
50 value suggests that this process is also not very important. Reinforcing the argument is the fact that the calculations of the electronic energy loss of protons in Al crystal
~i.e., lattice included! and in Al jellium30 differ by only 10%
differences for proton velocities smaller than 23108 cm/s.
Plasmon excitations that accompany the neutralization
near surfaces of slow ions ( n ! n F ) with high potential energy ~potential excitation! have been recently observed for
noble-gas ions on Al and Mg,31 and multiply-charged ions on
Al.32 This type of excitation was first predicted by Lucas and
Šunjic,33 and described theoretically34–37 for the case of surface plasmons. For Al and Mg, bulk-plasmon excitation cannot occur for stationary protons because the potential energy
available for excitation E n 5I P 8 2 f is insufficient31 ~I P 8 is
the ionization potential of H minus a ;2-eV image shift!.
The situation changes for moving protons. Here the energy
d P decay~ « p , v !
5
d« p
E
15 509
FIG. 7. Same as Fig. 6, but for Mg. d, H1 ; s, D1 .
distribution of valence electrons is shifted in the frame of the
ion, increasing the maximum energy release accompanying
neutralization, by ;m nn Fermi .
Plasmon excitation by electron capture can also occur in
the bulk of the solid, both for protons (H1→H) and for H
resulting from electron capture collisions in the solid
(H→H2). The probability that a plasmon is excited between
times t and t1dt is38
P ~ t ! 5F 1 ~ t !
dt
dt
0
1 1F ~ t ! 0 ,
t
t
~2!
where F 1 (t) @ F 0 (t) # is the fraction of H1~H! existing at
time t in the solid, and dt/ t 1 (dt/ t 0 ) is the probability that
H1~H! captures an electron with excitation of a plasmon. We
are interested in the spectrum of the electrons emitted by the
decay of this plasmon. In Eq. ~34.1! of Ref. 32 we find that
either of the transition rates 1/t 1 or 1/t 0 can be calculated as
1
t
1,0 5
E
vc
vp
dv
d P 1,0
.
dv
1
Then d P /d v gives us the rate at which plasmons of energy
\v in an energy range \ d v are excited in the Auger capture
process. We assume that all plasmons decay by imparting
their energy to a single electron. The probability that a plasmon of energy \v produces an electron above the Fermi
level at an energy « p , in an interval d« p , is written as
r ~ « p ! r ~ « p 2\ v ! Q ~ « p 2E F ! Q ~ E F 2« p 1\ v !
,
~3!
d« 8 r ~ « 8 ! r ~ « 8 1\ v ! Q ~ « 8 1\ v 2E F ! Q ~ E F 2« 8 !
where r~«! is the free-electron density of states, E F the
Fermi energy, and Q the step function. We also assume
that the plasmon produced at a depth z decays at the
same depth. We consider that the probability that one
electron is collected outside the surface is given by
1/2Te 2z/L , where z is the depth in the solid. The factor
1
2 takes into account that, on the average, only half of
the electrons travel toward the surface. T(«)5(«2W)/«
is the probability that an electron with energy « is trans-
mitted through the surface barrier of height W, and L(«)
is the calculated inelastic mean free path.38 The expression
for T follows the assumption that the electron motion inside
the solid is made isotropic by strong elastic scattering
at these low energies.39 Finally, the spectrum of electrons
produced by the decay of plasmons excited in the Auger
capture processes is calculated as the product of all probabilities integrated over the incoming path of the ion
z5 n t/cos(u)
15 510
S. M. RITZAU, R. A. BARAGIOLA, AND R. C. MONREAL
d g Ap ~ « p !
d« p
5
cos~ u !
n
3
E
E
dv
S
3 F1
dz
T ~ « p ! 2z/L
e
2
d P decay~ « p , v !
d« p
D
d P1
d P0
1F 0
,
dv
dv
~4!
where n is the ion velocity, and u the incidence angle with
respect to the surface normal. F 1 and F 0 have two contributions due to charge ‘‘equilibrium’’ at large depth, and
from the initial conditions at t50. As a further approximation we only consider the contribution of F 1eq and F 0eq
which we take from Ref. 38, and obtain the yield of electrons
from this capture processes as
g Ap 5
E
d« p
d g Ap
d« p
~5!
,
where the integration is performed on an energy window 61
eV, like in the experiment. The result of Eq. ~5! for Al is
plotted in Fig. 6. The bell shape of the curve is the consequence of the opposite behaviors of F 1eq and 1/n t 1 with
projectile velocity; when n increases, the H1 fraction increases and the capture probability per unit path length decreases. We find that the second term on the right-hand side
of Eq. ~2! only contributes appreciably to the plasmon intensity for projectile energies less than 16 keV/amu; above this
value, the first term dominates. It can be seen from Fig. 6
that plasmon excitation by electron capture is not the dominant factor determining the existence of plasmon excitation
below n th .
Finally, we consider plasmon excitation by fast secondary
electrons produced by the projectile. One source of energetic
electrons is the Auger decay of L-shell vacancies in target
atoms, excited by the incoming projectile. The cross section
for production of LVV Auger electrons by protons at velocities just below n th is s A ;4310218 cm2/atom for Mg,15 corresponding to a mean free path between excitations of 425 Å.
Thus the excitation probability is only 0.02 over the 9-Å
mean escape depth39 of 10-eV electrons ~representing plasmon decay!. The value is even lower for Al, where the cross
section for L-shell excitation near n th is about a factor of 4
smaller.15 Therefore, the very small excitation probability of
inner shells strongly discounts Auger electrons as a significant mechanism for plasmon excitation below n th .
A more abundant source of energetic electrons is the binary proton-electron interactions in the solid. To calculate
the electron yield due to the decay of electron-excited plasmons g ep , we consider a proton moving with velocity n in in
the solid near the surface, exciting electrons of energy « e
with probability P in( n in« e ). P in is taken to be independent of
S D E E
d g ep
d«
5
d« e
out
3T ~ « !
`
0
1
ne
dz
P ~ n ,« !
cos~ u ! in in e
E
vc
vp
dv
PRB 59
depth z since protons suffer negligible angular scattering and
energy loss over the electron escape depth ~a few nm! at
these incident velocities.39 We again assume that the electron
motion inside the solid is made isotropic by strong elastic
scattering at these low energies, so that the electron has an
equal probability of traveling toward or away from the surface.
Our treatment of the electrons will be slightly different for
these two directions. We first consider a fast electron headed
toward the surface. After traveling some distance, it may
excite a plasmon at a depth z 8 with a probability P 1 given by
the product of the probability that it does not suffer a collision on its way to z 8 , and the probability that it will produce
a plasmon at z 8 :
S
P 1 5exp 2
D
~ z2z 8 ! dz 8
,
L
lp
~6!
where l p (« e ) is the mean free path to excite a plasmon, and
L(« e ) is the total inelastic mean free path. Equation ~6! assumes that plasmons can only be excited in the first collision
event; this is because an electron loses a large fraction of its
energy in one collision, and thus it is unable to excite a
plasmon in a second one. Thus an energy-loss event, either
by exciting a plasmon or another electron, is sufficient to
remove the electron from the high-energy tail, and should be
a good approximation at the energies of interest, ,40 eV for
Al. To determine l p , we use the random-phaseapproximation ~RPA! expression38
1
1
5
lp ne
E
vc
vp
dv
d P~ «e ,v !
,
dv
~7!
where n e is the electron velocity, v p and v c are the plasmon
frequencies at k50 and at the cut-off momentum k c , respectively, and d P(« e , v )/d v is the rate at which an electron of
energy « e will produce a plasmon of energy \v.
We assume that the plasmon produced at z 8 decays at z 8
as well, producing an electron with energy «. The probability
that a secondary electron of energy « e produces a plasmon of
energy \v that decays into an electron of energy « is then
given by the product
P 25
d P ~ « e , v ! d P decay~ «, v !
,
3
dv
d«
~8!
where the second term is given by Eq. ~3!. Again, the
~plasmon-decay! electron has an equal probability of traveling toward the surface or away from it. Considering only
those electrons which are heading to the surface, we apply an
attenuation factor of exp@2z8/L(«)# to account for transport
to the surface. We combine the results of Eqs. ~6!–~8! and
integrate over z, z 8 , v, and « e to obtain the number of electrons of energy «.
E
S
D S
1
z2z 8 1
z8
exp 2
dz 8 exp 2
2
L~ «e! 2
L~ « !
0
z
d P ~ « e , v ! d P decay~ «, v !
.
dv
d«
D
~9!
PRB 59
PROTON-INDUCED KINETIC PLASMON EXCITATION . . .
To determine P in( n in ,« e ) we use the measured tail of N(E)
at energies higher than the minimum value to excite plasmons, which is ;18.7 ~12.1! eV above the vacuum level for
Al ~Mg! in the RPA. This tail has the form N t (E)5B/E p ,
with « e 5E1W. This gives
P in~ n in ,« e ! 5
2B cos~ u !
.
L~ « e !E pT~ « e !
~10!
Substituting Eq. ~10! into Eq. ~9! and integrating in z and z 8 ,
we find
S D E
d g ep
d«
5
d« e
out
3
B 1 T~ « ! L~ « !
E p 2 T~ «e! ne
E
vc
vp
dv
d P~ «e ,v !
dv
d P decay~ «, v !
.
d«
~11!
While we ignore the plasmon-decay electrons that are headed
into the solid, we must now consider the fast secondary electrons that were headed in that direction. The development for
these electrons is exactly the same as for the proton-excited
electrons which were headed out of the solid, using the corresponding exponential factor in Eq. ~6!. We combine these
electrons with those in Eq. ~11! to obtain the energy distribution of electrons due to plasmon decay:
d g ep
d«
5
S
D
E
d« e
B T ~ « ! 11L ~ « e ! /2L ~ « ! L ~ « !
E p T ~ « e ! 11L ~ « e ! /L ~ « ! n e
3
E
dv
vc
vp
d P ~ « e , v ! d P decay~ «, v !
.
3
dv
d«
~12!
Using linear-response theory, we find d P(« e , v )/d v , the
rate at which a particle excites plasmons of energy v. It is
given essentially by Eq. ~6.1! of Ref. 38 integrated in q and
with Im@21/«(q, v ) # evaluated only on the plasmon line.
Numerical integration over « gives g ep . Because we obtain
d g ep /d«, which is a calculation of N p (E), we can also determine values of C( v 0 ) for Al and Mg. We find C( n 0 ) range
from 6.75 to 7.1 over the energy range of interest for Al, and
from 3.9 to 4.9 for Mg.
Calculated values of d g ep are shown in Figs. 6 and 7 for
Al and Mg, respectively. For Al, the agreement with experiment at low n suggests that energetic secondary electrons are
an important source of plasmons, and can explain the discrepancy between theory and experiment below n th . For Mg,
we also obtain good agreement at the lower velocities, but
the model overestimates the yields at velocities above the
threshold for direct plasmon excitation. A plausible source
for this discrepancy is that we have not considered that due
to the begrenzung effect,25,40 near the surface part of the
excitation of plasmons that we calculate actually results in
surface plasmons, which we do not measure. This effect is
more important in Mg and at high proton velocities where
the mean free path of the electrons is smaller due to a larger
relative contribution of high-energy electrons. We note that
there are other uncertainties in the model, like the localization of the plasmon decay, and the simplified treatment of
electron transport. Nevertheless, the fact that theory and experiment are close at low velocities, where the contribution
15 511
of the higher-energy electrons is smaller, suggest that energetic secondary electrons are the main source of plasmon
excitations at velocities lower than n th . The importance of
secondary electrons in producing relatively high-energy excitations in metals parallels that found in the efficient ionization of dense gases or insulators. In condensed Ar ~band gap
14.2 eV!, half the ionizations are produced by secondary
electrons for 100-keV incident protons.2
The mechanism of plasmon excitation due to fast electrons should also need a velocity above a threshold value.
This results because the maximum energy transfer from a
proton to an electron at the Fermi level, 2m n ( n 2 n Fermi)
~Ref. 17!, must lead to a final electron energy exceeding the
minimum energy for plasmon excitation. The value of this
8 is 0.74(0.64)3108 cm/s for Al ~Mg!, lower
threshold n th
than n th and than the smallest velocities used in this study.
These thresholds correspond to 2.9 and 2.1 keV/amu for Al
and Mg, respectively.
We note that in Figs. 6 and 7 the experiments do not show
a discontinuity at the threshold for direct plasmon excitation,
as predicted by Rösler’s theory.3 Possible reasons for this are
the neglect of projectile neutralization and the limitations of
the free-electron RPA. The effect of projectile neutralization
would be a decrease in the plasmon yield that is more pronounced at the lowest velocities, thus smoothing the onset at
the threshold. However, RPA theories of electronic energy
loss that take charge exchange into account also give a discontinuity at n th ~e.g., Ref. 41!. Thus we are led to the conclusion that the abrupt threshold for direct plasmon excitation is a characteristic of this type of free-electron
approximation.
In conclusion, we have observed that plasmon excitation
and decay in collisions of 5–100-keV protons with Mg and
Al metals is an important electron emission mechanism. The
energy dependence of plasmon excitation agrees with the
theory of Rösler3 at higher energies, but we observe significant plasmon excitation at velocities below the threshold predicted by theory ~40 and 25 keV/amu for Al and Mg, respectively!. We analyze several causes for the discrepancy, and
conclude that the most plausible one is plasmon excitation by
fast secondary electrons resulting from binary ion-electron
collisions. This result has several implications: ~i! Since the
maximum electron energy depends on the projectile velocity,
there is a threshold velocity for this secondary plasmon excitation that is substantially lower than that for direct excitation. ~ii! Plasmon excitation by secondary electrons will be
particularly important when using highly charged projectiles,
since they are important sources of energetic Auger electrons. ~iii! There appears to be a significant discrepancy with
current theories of energy loss regarding the onset of the
contribution of direct plasmon excitations.
ACKNOWLEDGMENTS
We thank M. Rösler, S. Schnatterly, and J. Garcı́a de
Abajo for useful discussions. This work was supported by
the National Science Foundation, Division of Materials Research, the Southwest Research Institute, Iberdrola S.A., and
the Spanish Comisión Interministerial de Ciencia y Tecnologı́a, Contract No. PB97-0044.
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